Ed Murray/The Star-LedgerAt this May press conference, N.J. Senate President Stephen Sweeney (D-Gloucester), left, is all smiles with Gov. Chris Christie, but Senate Democrats may challenge the governor's proposed budget with a spending plan of their own, sources said.

TRENTON — Senate Democrats are thinking of introducing their own budget that would increase school financing by as much as $1.1 billion, including about $600 million for non-Abbott school districts, according to four people familiar with the plan.

The money would come from a combination of additional revenue, some cuts in spending, and possibly a millionaire’s tax, said the sources, who requested anonymity because they are not authorized to discuss the plan.

The proposal is emerging less than three weeks after the state Supreme Court ordered the state to increase financing for poor school districts, known as Abbott districts, by $500 million, and with three weeks to go until the legislature is required to approve a budget for the next fiscal year.

The plan was unveiled by State Senate President Stephen Sweeney at a recent Senate Democratic caucus, the sources said. Derek Roseman, a spokesman for the Senate Democrats, said he would not comment on internal deliberations, nor would he confirm or deny the proposal.

The state Supreme Court stopped short of ordering the restoration of the full $1.7 billion in cuts that Gov. Chris Christie relied on to balance this year’s budget. The governor said he would comply with the order after giving some mixed signals, but left it to the Democrat-controlled legislature to work out the details — as long as there is no tax increase.

The Senate plan would satisfy the court ruling as well as provide additional money for up to 240 other districts that are not spending as much as they should be under the school funding formula. Many of those districts have high numbers of at-risk students, but were not granted any financial relief by the court.

David Sciarra, executive director of the Education Law Center, who has lobbied lawmakers and Christie to restore the funds, said the additional money would go to all students who need it, not just to those in the poorer districts.

"If this were done it would go a long way towards fulfilling the commitment made by the Legislature in the (school funding) formula, which was to make sure that at-risk students, whichever district they were in, received the funding they were entitled to receive," he said.

Woodbridge, a district with 13,000 students, about 30 percent of whom are low income, would receive $18.6 million in additional aid, he said, while Hamilton Township in Mercer County, also with about 13,000 students, would get an additional $9.8 million.

To pay for the proposal, Democratic Senators would rely on the revenue estimates provided by the non-partisan Office of Legislative Services instead of the less optimistic figures put forth by the Christie administration, sources say. The OLS figure of $913 million is $400 million higher than the administration’s figure.

The Democrats would also rely on up to $300 million in budget cuts that have not yet been determined, sources said. A millionaire’s tax has been discussed despite Christie’s objection to it.

The sources said Democrats are divided on whether to pursue the strategy in part because it would require them to sponsor the budget and make it difficult for them to criticize the governor for his handling of the state’s finances.

Last year, the budget was approved with the slimmest of Democratic support, handing Republicans ownership of a plan that included huge cuts and froze property tax rebates.

Lawmakers have until June 30 to approve Christie’s $29.6 billion budget for the fiscal year that begins July 1. Christie has called for tripling current property tax rebates next year, but only if legislators agree to make changes to health and pension benefits for state and municipal workers.

Kevin Roberts, a spokesman for the governor, said he wouldn’t comment on a plan put forward by lawmakers until it was more than a rumor.

"We will review a budget bill once the legislature fulfills its own obligation to pass such legislation and it reaches the governor’s desk for consideration," Roberts said in an e-mail message. "We won’t be responding to abstract proposals in the interim."

A spokesman for the Assembly Democrats, Tom Hester Jr., said the governor’s budget puts the heaviest burden on working-class residents, and that lawmakers are committed to doing everything possible to resolve that problem.

"But as everyone is also well aware, nothing gets to the governor’s desk without garnering Assembly support," Hester said. "We look forward to a cooperative discussion in the month ahead built around the goal of advocating for working class residents."